Abstract: A process for preparing an aqueous polymer dispersion by free-radical polymerization of compounds I and II whose individual solubility in water is very different by the miniemulsion polymerization technique, in which process the reaction mixture is agitated by an external circuit which leads from and back again to the reaction vessel and comprises at least one low-shear pump and at least one heat exchanger having an essentially laminar flow profile. The copolymers prepared in accordance with the invention can be produced in a good yield within short times and exhibit good performance properties.